Cambridge International AS and A Level Mathematics Pure Mathematics 1
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Sophie Goldie
Roger Porkess
pure math
Hodder
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Cambridge International AS and A Level Mathematics Pure Mathematics 1
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Chapter 1: Algebra
Theory
Page 10
Background Algebra
Theory
Page 10
Linear Equations
Theory
Page 15
Changing the Subject of a Formula
Theory
Page 19
Quadratic Equations
Theory
Page 21
Solving Quadratic Equations
Theory
Page 26
Equations That Cannot Be Factorised
Theory
Page 29
The Graphs of Quadratic Functions
Theory
Page 31
The Quadratic Formula
Theory
Page 34
Simultaneous Equations
Theory
Page 38
Inequalities
Theory
Page 43
Chapter 2: Co-ordinate Geometry
Theory
Page 47
Co-ordinates
Theory
Page 47
Plotting, Sketching and Drawing
Theory
Page 48
The Gradient of a Line
Theory
Page 48
The Distance Between Two Points
Theory
Page 50
The Mid-point of a Line Joining Two Points
Theory
Page 51
The Equation of a Straight Line
Theory
Page 55
Finding the Equation of a Line
Theory
Page 58
The Intersection of Two Lines
Theory
Page 65
Drawing Curves
Theory
Page 72
The Intersection of a Line and a Curve
Theory
Page 79
Chapter 3: Sequences and Series
Theory
Page 84
Definitions and Notation
Theory
Page 85
Arithmetic Progressions
Theory
Page 86
Geometric Progressions
Theory
Page 93
Binomial Expansions
Theory
Page 104
Chapter 4: Functions
Theory
Page 115
The Language of Functions
Theory
Page 115
Composite Functions
Theory
Page 121
Inverse Functions
Theory
Page 124
Chapter 5: Differentiation
Theory
Page 132
The Gradient of a Curve
Theory
Page 132
Finding the Gradient of a Curve
Theory
Page 133
Finding the Gradient from First Principles
Theory
Page 135
Differentiating by Using Standard Results
Theory
Page 140
Using Differentiation
Theory
Page 143
Tangents and Normals
Theory
Page 149
Maximum and Minimum Points
Theory
Page 155
Increasing and Decreasing Functions
Theory
Page 159
Points of Inflection
Theory
Page 162
The Second Derivative
Theory
Page 163
Applications
Theory
Page 169
The Chain Rule
Theory
Page 176
Chapter 6: Integration
Theory
Page 182
Reversing Differentiation
Theory
Page 182
Finding the Area Under a Curve
Theory
Page 188
Area as the Limit of a Sum
Theory
Page 191
Areas Below the x Axis
Theory
Page 202
The Area Between Two Curves
Theory
Page 206
The Area Between a Curve and the y Axis
Theory
Page 211
The Reverse Chain Rule
Theory
Page 212
Improper Integrals
Theory
Page 215
Finding Volumes by Integration
Theory
Page 217
Chapter 7: Trigonometry
Theory
Page 225
Trigonometry Background
Theory
Page 225
Trigonometrical Functions
Theory
Page 226
Trigonometrical Functions for Angles of Any Size
Theory
Page 231
The Sine and Cosine Graphs
Theory
Page 235
The Tangent Graph
Theory
Page 237
Solving Equations Using Graphs of Trigonometrical Functions
Theory
Page 238
Circular Measure
Theory
Page 244
The Length of an Arc of a Circle
Theory
Page 248
The Area of a Sector of a Circle
Theory
Page 248
Other Trigonometrical Functions
Theory
Page 253
Chapter 8: Vectors
Theory
Page 263
Vectors in Two Dimensions
Theory
Page 263
Vectors in Three Dimensions
Theory
Page 267
Vector Calculations
Theory
Page 271
The Angle Between Two Vectors
Theory
Page 280
Answers
Answer
Page 289
Index
Other
Page 319
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